Control theoretic approach to random branching walk models arising in molecular biology

Abstract

Techniques commonly used in control theory based on Laplace transforms, spectral analysis, semigroup for state equations, methods of analysis and design of feedback systems enable to characterize the asymptotic behavior of telomeres shortening of which is supposed to be the mechanism of aging and death and cancer cells with increasing number of copies genes responsible for coding proteins causing drug removal or metabolisation. We model these two phenomena by branching random walk processes representing dynamical evolution of particles in them that leads to the systems of infinitely many linear or bilinear state equations. Their transformation into equivalent integro-differential or integral equations allow to design control strategies which are optimal in the sense of some performance indices.